11L 12s

↖ 10L 11s	↑ 11L 11s	12L 11s ↗
← 10L 12s	11L 12s	12L 12s →
↙ 10L 13s	↓ 11L 13s	12L 13s ↘

Scale structure
Step pattern	LsLsLsLsLsLsLsLsLsLsLss ssLsLsLsLsLsLsLsLsLsLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	2\23 to 1\11 (104.3 ¢ to 109.1 ¢)
Dark	10\11 to 21\23 (1090.9 ¢ to 1095.7 ¢)
TAMNAMS information
Related to	1L 9s (antisinatonic)
With tunings	2:1 to 5:2 (minihard)
Related MOS scales
Parent	11L 1s
Sister	12L 11s
Daughters	23L 11s, 11L 23s
Neutralized	22L 1s
2-Flought	34L 12s, 11L 35s
Equal tunings
Equalized (L:s = 1:1)	2\23 (104.3 ¢)
Supersoft (L:s = 4:3)	7\80 (105.0 ¢)
Soft (L:s = 3:2)	5\57 (105.3 ¢)
Semisoft (L:s = 5:3)	8\91 (105.5 ¢)
Basic (L:s = 2:1)	3\34 (105.9 ¢)
Semihard (L:s = 5:2)	7\79 (106.3 ¢)
Hard (L:s = 3:1)	4\45 (106.7 ¢)
Superhard (L:s = 4:1)	5\56 (107.1 ¢)
Collapsed (L:s = 1:0)	1\11 (109.1 ¢)
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11L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 12 small steps, repeating every octave. 11L 12s is a great-grandchild scale of 1L 9s, expanding it by 13 tones. Generators that produce this scale range from 104.3 ¢ to 109.1 ¢, or from 1090.9 ¢ to 1095.7 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 11L 12s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 52.2 ¢
	Major 1-mosstep	M1ms	L	52.2 ¢ to 109.1 ¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0 ¢ to 104.3 ¢
	Perfect 2-mosstep	P2ms	L + s	104.3 ¢ to 109.1 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	109.1 ¢ to 156.5 ¢
	Major 3-mosstep	M3ms	2L + s	156.5 ¢ to 218.2 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	109.1 ¢ to 208.7 ¢
	Major 4-mosstep	M4ms	2L + 2s	208.7 ¢ to 218.2 ¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	218.2 ¢ to 260.9 ¢
	Major 5-mosstep	M5ms	3L + 2s	260.9 ¢ to 327.3 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	218.2 ¢ to 313.0 ¢
	Major 6-mosstep	M6ms	3L + 3s	313.0 ¢ to 327.3 ¢
7-mosstep	Minor 7-mosstep	m7ms	3L + 4s	327.3 ¢ to 365.2 ¢
	Major 7-mosstep	M7ms	4L + 3s	365.2 ¢ to 436.4 ¢
8-mosstep	Minor 8-mosstep	m8ms	3L + 5s	327.3 ¢ to 417.4 ¢
	Major 8-mosstep	M8ms	4L + 4s	417.4 ¢ to 436.4 ¢
9-mosstep	Minor 9-mosstep	m9ms	4L + 5s	436.4 ¢ to 469.6 ¢
	Major 9-mosstep	M9ms	5L + 4s	469.6 ¢ to 545.5 ¢
10-mosstep	Minor 10-mosstep	m10ms	4L + 6s	436.4 ¢ to 521.7 ¢
	Major 10-mosstep	M10ms	5L + 5s	521.7 ¢ to 545.5 ¢
11-mosstep	Minor 11-mosstep	m11ms	5L + 6s	545.5 ¢ to 573.9 ¢
	Major 11-mosstep	M11ms	6L + 5s	573.9 ¢ to 654.5 ¢
12-mosstep	Minor 12-mosstep	m12ms	5L + 7s	545.5 ¢ to 626.1 ¢
	Major 12-mosstep	M12ms	6L + 6s	626.1 ¢ to 654.5 ¢
13-mosstep	Minor 13-mosstep	m13ms	6L + 7s	654.5 ¢ to 678.3 ¢
	Major 13-mosstep	M13ms	7L + 6s	678.3 ¢ to 763.6 ¢
14-mosstep	Minor 14-mosstep	m14ms	6L + 8s	654.5 ¢ to 730.4 ¢
	Major 14-mosstep	M14ms	7L + 7s	730.4 ¢ to 763.6 ¢
15-mosstep	Minor 15-mosstep	m15ms	7L + 8s	763.6 ¢ to 782.6 ¢
	Major 15-mosstep	M15ms	8L + 7s	782.6 ¢ to 872.7 ¢
16-mosstep	Minor 16-mosstep	m16ms	7L + 9s	763.6 ¢ to 834.8 ¢
	Major 16-mosstep	M16ms	8L + 8s	834.8 ¢ to 872.7 ¢
17-mosstep	Minor 17-mosstep	m17ms	8L + 9s	872.7 ¢ to 887.0 ¢
	Major 17-mosstep	M17ms	9L + 8s	887.0 ¢ to 981.8 ¢
18-mosstep	Minor 18-mosstep	m18ms	8L + 10s	872.7 ¢ to 939.1 ¢
	Major 18-mosstep	M18ms	9L + 9s	939.1 ¢ to 981.8 ¢
19-mosstep	Minor 19-mosstep	m19ms	9L + 10s	981.8 ¢ to 991.3 ¢
	Major 19-mosstep	M19ms	10L + 9s	991.3 ¢ to 1090.9 ¢
20-mosstep	Minor 20-mosstep	m20ms	9L + 11s	981.8 ¢ to 1043.5 ¢
	Major 20-mosstep	M20ms	10L + 10s	1043.5 ¢ to 1090.9 ¢
21-mosstep	Perfect 21-mosstep	P21ms	10L + 11s	1090.9 ¢ to 1095.7 ¢
	Augmented 21-mosstep	A21ms	11L + 10s	1095.7 ¢ to 1200.0 ¢
22-mosstep	Minor 22-mosstep	m22ms	10L + 12s	1090.9 ¢ to 1147.8 ¢
	Major 22-mosstep	M22ms	11L + 11s	1147.8 ¢ to 1200.0 ¢
23-mosstep	Perfect 23-mosstep	P23ms	11L + 12s	1200.0 ¢

Generator chain

Generator chain of 11L 12s

Bright gens	Scale degree	Abbrev.
33	Augmented 20-mosdegree	A20md
32	Augmented 18-mosdegree	A18md
31	Augmented 16-mosdegree	A16md
30	Augmented 14-mosdegree	A14md
29	Augmented 12-mosdegree	A12md
28	Augmented 10-mosdegree	A10md
27	Augmented 8-mosdegree	A8md
26	Augmented 6-mosdegree	A6md
25	Augmented 4-mosdegree	A4md
24	Augmented 2-mosdegree	A2md
23	Augmented 0-mosdegree	A0md
22	Augmented 21-mosdegree	A21md
21	Major 19-mosdegree	M19md
20	Major 17-mosdegree	M17md
19	Major 15-mosdegree	M15md
18	Major 13-mosdegree	M13md
17	Major 11-mosdegree	M11md
16	Major 9-mosdegree	M9md
15	Major 7-mosdegree	M7md
14	Major 5-mosdegree	M5md
13	Major 3-mosdegree	M3md
12	Major 1-mosdegree	M1md
11	Major 22-mosdegree	M22md
10	Major 20-mosdegree	M20md
9	Major 18-mosdegree	M18md
8	Major 16-mosdegree	M16md
7	Major 14-mosdegree	M14md
6	Major 12-mosdegree	M12md
5	Major 10-mosdegree	M10md
4	Major 8-mosdegree	M8md
3	Major 6-mosdegree	M6md
2	Major 4-mosdegree	M4md
1	Perfect 2-mosdegree	P2md
0	Perfect 0-mosdegree Perfect 23-mosdegree	P0md P23md
−1	Perfect 21-mosdegree	P21md
−2	Minor 19-mosdegree	m19md
−3	Minor 17-mosdegree	m17md
−4	Minor 15-mosdegree	m15md
−5	Minor 13-mosdegree	m13md
−6	Minor 11-mosdegree	m11md
−7	Minor 9-mosdegree	m9md
−8	Minor 7-mosdegree	m7md
−9	Minor 5-mosdegree	m5md
−10	Minor 3-mosdegree	m3md
−11	Minor 1-mosdegree	m1md
−12	Minor 22-mosdegree	m22md
−13	Minor 20-mosdegree	m20md
−14	Minor 18-mosdegree	m18md
−15	Minor 16-mosdegree	m16md
−16	Minor 14-mosdegree	m14md
−17	Minor 12-mosdegree	m12md
−18	Minor 10-mosdegree	m10md
−19	Minor 8-mosdegree	m8md
−20	Minor 6-mosdegree	m6md
−21	Minor 4-mosdegree	m4md
−22	Diminished 2-mosdegree	d2md
−23	Diminished 23-mosdegree	d23md
−24	Diminished 21-mosdegree	d21md
−25	Diminished 19-mosdegree	d19md
−26	Diminished 17-mosdegree	d17md
−27	Diminished 15-mosdegree	d15md
−28	Diminished 13-mosdegree	d13md
−29	Diminished 11-mosdegree	d11md
−30	Diminished 9-mosdegree	d9md
−31	Diminished 7-mosdegree	d7md
−32	Diminished 5-mosdegree	d5md
−33	Diminished 3-mosdegree	d3md

Modes

Scale degrees of the modes of 11L 12s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
22|0	1	LsLsLsLsLsLsLsLsLsLsLss	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Perf.
21|1	3	LsLsLsLsLsLsLsLsLsLssLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.
20|2	5	LsLsLsLsLsLsLsLsLssLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
19|3	7	LsLsLsLsLsLsLsLssLsLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
18|4	9	LsLsLsLsLsLsLssLsLsLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
17|5	11	LsLsLsLsLsLssLsLsLsLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
16|6	13	LsLsLsLsLssLsLsLsLsLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
15|7	15	LsLsLsLssLsLsLsLsLsLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
14|8	17	LsLsLssLsLsLsLsLsLsLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
13|9	19	LsLssLsLsLsLsLsLsLsLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
12|10	21	LssLsLsLsLsLsLsLsLsLsLs	Perf.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
11|11	23	sLsLsLsLsLsLsLsLsLsLsLs	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
10|12	2	sLsLsLsLsLsLsLsLsLsLssL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Perf.
9|13	4	sLsLsLsLsLsLsLsLsLssLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Min.	Perf.	Min.	Perf.
8|14	6	sLsLsLsLsLsLsLsLssLsLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
7|15	8	sLsLsLsLsLsLsLssLsLsLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
6|16	10	sLsLsLsLsLsLssLsLsLsLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
5|17	12	sLsLsLsLsLssLsLsLsLsLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
4|18	14	sLsLsLsLssLsLsLsLsLsLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
3|19	16	sLsLsLssLsLsLsLsLsLsLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
2|20	18	sLsLssLsLsLsLsLsLsLsLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
1|21	20	sLssLsLsLsLsLsLsLsLsLsL	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
0|22	22	ssLsLsLsLsLsLsLsLsLsLsL	Perf.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 11L 12s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\23						104.348	1095.652	1:1	1.000	Equalized 11L 12s
					11\126	104.762	1095.238	6:5	1.200
				9\103		104.854	1095.146	5:4	1.250
					16\183	104.918	1095.082	9:7	1.286
			7\80			105.000	1095.000	4:3	1.333	Supersoft 11L 12s
					19\217	105.069	1094.931	11:8	1.375
				12\137		105.109	1094.891	7:5	1.400
					17\194	105.155	1094.845	10:7	1.429
		5\57				105.263	1094.737	3:2	1.500	Soft 11L 12s
					18\205	105.366	1094.634	11:7	1.571
				13\148		105.405	1094.595	8:5	1.600
					21\239	105.439	1094.561	13:8	1.625
			8\91			105.495	1094.505	5:3	1.667	Semisoft 11L 12s
					19\216	105.556	1094.444	12:7	1.714
				11\125		105.600	1094.400	7:4	1.750
					14\159	105.660	1094.340	9:5	1.800
	3\34					105.882	1094.118	2:1	2.000	Basic 11L 12s Scales with tunings softer than this are proper
					13\147	106.122	1093.878	9:4	2.250
				10\113		106.195	1093.805	7:3	2.333
					17\192	106.250	1093.750	12:5	2.400
			7\79			106.329	1093.671	5:2	2.500	Semihard 11L 12s
					18\203	106.404	1093.596	13:5	2.600
				11\124		106.452	1093.548	8:3	2.667
					15\169	106.509	1093.491	11:4	2.750
		4\45				106.667	1093.333	3:1	3.000	Hard 11L 12s
					13\146	106.849	1093.151	10:3	3.333
				9\101		106.931	1093.069	7:2	3.500
					14\157	107.006	1092.994	11:3	3.667
			5\56			107.143	1092.857	4:1	4.000	Superhard 11L 12s
					11\123	107.317	1092.683	9:2	4.500
				6\67		107.463	1092.537	5:1	5.000
					7\78	107.692	1092.308	6:1	6.000
1\11						109.091	1090.909	1:0	→ ∞	Collapsed 11L 12s

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